In digital signal processing, an input signal may be sampled by a sampling circuit at a particular sampling frequency. The sampling frequency is defined as the number of samples of the input signal obtained in one second (measured in hertz). If enough samples are taken of the input signal over a given period of time (e.g., if the sampling frequency of the sampling circuit is high enough), then the input signal may be reconstructed using the samples. In particular embodiments, the sampling frequency may be dependent upon the circuitry employed by the sampling circuit to obtain the samples of the input signal. For example, if the circuitry employed by the sampling circuit cannot operate at a high enough frequency to accommodate a particular input signal (e.g., if the sampling circuit cannot take samples fast enough to account for the data changes in the input signal), then a portion of the data contained in the input signal may be lost or damaged during the sampling. Consequently, “maximum frequency of operation” may be one of the performance metrics used to gauge the operational ability of a sampling circuit.
As the maximum frequency of operation of a sampling circuit increases, the samples of an input signal are compressed closer to one another in time. Ideally, samples of the input signal represent “snapshots” of individual point values along the input signal at particular moments in time. As an example and not by way of limitation, if a sampling circuit were to obtain samples of an input signal using a series of perfect impulses (e.g., using a dirac comb), then each sample would represent a single, mutually exclusive, point along the input signal. However, the ability to obtain perfectly discrete samples of an input signal may be limited by the operational ability of the sampling circuit. As an example and not by way of limitation, the aperture time of the sampling circuit (e.g., the temporal width of each sample obtained by the sampling circuit) may not be instantaneous due to various operational constraints inherent in the sampling circuit such as operational delays associated with particular circuit topologies or delays associated with the operation of particular electrical components of the circuit. Consequently, “aperture time” may be another performance metric used to gauge the operational ability of a sampling circuit.